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sobereva

Tian Lu (Multiwfn developer)

From: Athens, Greece

Registered: 2017-09-11

Posts: 2,256

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Reasonableness of wB97XD for wavefunction analyses

A Multiwfn user asked me if wB97XD is suitable for calculation of delocalization index using Multiwfn and its comparison with GGA and hybrid-GGA functionals. My reply is also provided here, which may be also useful for other Multiwfn users.

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wB97XD is a very reasonable choice. Its improvement of representation of wavefunction over (meta-)GGA and common hybrid (meta-)GGA depends on the specific functional and the system.

When a (meta-)(hybrid-)GGA shows evident delocalization error (also known as self-interaction error, SIE) for a system, the improvement of wB97XD is significant. Representative examples include [18]annulene and cyclo[18]carbon. In Angew. Chem. Int. Ed. 2004, 43, 4200–4206, it is shown that B3LYP (20% global HF component) cannot give reasonable structure of [18]annulene, while I found the geometry optimized by wB97XD is fully correct. cyclo[18]carbon cannot be reasonably represented by any functional with insufficient HF composition at long-range, e.g. B3LYP (20% HF) and PBE0 (25% HF), while BHandHLYP (50% HF), M06-2X (54% HF) and wB97XD (22.2% to 100% HF from short-range limit to long-range limit) work reasonably, see my study and review about this system: Carbon, 165, 468-475 (2020), Acc. Mater. Res., 6, 1220−1231 (2025).

(hybrid-)(meta-)GGA functionals with insufficient HF composition at long-range tend to severely overestimate electronic delocalization of the aforemention systems, not only the resulting wavefunction is not reasonable, but also the optimized geometry is qualitatively wrong (strong tendency towards planarization and bond length equalization). For more information about the poor performance of these functionals, see review about delocalization error: WIREs Comput Mol Sci. 2022;e1631.